The COGENT project aims to tackle a range of scientific challenges including:
- Obtaining full explicit information on the cohomology of several families of arithmetic groups.
- Circumventing the exponential complexity of current computational methods.
- Implementing the action of Hecke operators.
- Explicitly studying algebraic K-groups and related conjectures, and connecting elements in algebraic K-groups and in homology.
- Testing and refining the integral Langlands Program.
- Formally verifying intricate proofs and computer-aided computations.
- Identifying suitable applications of motivic cohomology and group theory to cryptography.